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In this paper, we investigate the stability of the linear wave equation where one part of the boundary, which is seen as a lower-dimensional Riemannian manifold, is governed by a coupled wave equation, while the other part is subject to a…
Much of modern condensed matter physics is understood in terms of elementary excitations, or quasiparticles - fundamental quanta of energy and momentum. Various strongly-interacting atomic systems are successfully treated as a collection of…
In this paper we present a novel quasi-exactly solvable model with symmetric inverted potentials which are unbounded from below. The quasi-exactly solvable states are shown to be total transmission (or reflectionless) modes. From these…
Motivated by the study of conditional stability of traveling waves, we give an elementary $H^2$ center stable manifold construction for quasilinear parabolic PDE, sidestepping apparently delicate regularity issues by the combination of a…
In this paper we give explicit examples of bounded domains that satisfy the quasihyperbolic boundary condition and calculate the values for the constants. These domains are also John domains and we calculate John constants as well. The…
Bound state formation is a classic feature of quantum mechanics, where a particle localizes in the vicinity of an attractive potential. This is typically understood as the particle lowering its potential energy. In this article, we discuss…
Attempts to disentangle shear-flow turbulence often focus on identifying relatively simple solutions, such as travelling waves or periodic orbits. We show, however, that capturing multiscale features requires considering states at least as…
The objective of this work is to investigate the unexplored laminar-to-turbulent transition of a heated flat-plate boundary layer with a fluid at supercritical pressure. Two temperature ranges are considered: a subcritical case, where the…
The weakly nonlinear dynamics of the free surface of a dielectric liquid in an electric field directed tangentially to the unperturbed boundary is investigated numerically. Within the framework of the strong field model, when the effects of…
We prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case…
In this paper we consider a semi-linear, defocusing, shifted wave equation on the hyperbolic space \[ \partial_t^2 u - (\Delta_{{\mathbb H}^n} + \rho^2) u = - |u|^{p-1} u, \quad (x,t)\in {\mathbb H}^n \times {\mathbb R}; \] and introduce a…
We prove the existence of the modified wave operators for a scalar quasilinear wave equation satisfying the weak null condition. This is accomplished in three steps. First, we derive a new reduced asymptotic system for the quasilinear wave…
The quasi-isotropic inhomogeneous solution of the Einstein equations near a cosmological singularity in the form of a series expansion in the synchronous system of reference, first found by Lifshitz and Khalatnikov in 1960, is generalized…
Analogue systems are a powerful instrument to investigate and understand in a controlled setting many general-relativistic effects. Here, we focus on superradiant-triggered instabilities and quasi-normal modes. We consider a compressible…
In this thesis we investigate the instabilities of superfluids at finite superflow by means of a hydrodynamical approach. We find that at a finite value of the background superfluid velocity a hydrodynamic collective mode crosses to the…
The dynamics of large eddies in the atmosphere and oceans is described by the surface quasi geostrophic equation, which is reminiscent of the Euler equations. Thermal fronts build up rapidly. Two different numerical methods combined with…
We develop a quasi-classical theory of high harmonic generation in semiconductors based on an interband current that has been transformed from Bloch to Wannier basis. The Wannier quasi-classical approach reveals a complete picture of the…
In this work, we consider the inverse problem of simultaneously recovering two classes of quasilinear terms appearing in a parabolic equation from boundary measurements. It is motivated by several industrial and scientific applications,…
We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and…
Quasiperiodic media is a class of almost periodic media which is generated from periodic media through a "cut and project" procedure. Bloch waves are typically defined through a direct integral decomposition of periodic operators. A…